Fourth, Section  proves a sharp asymptotic optimality result in settings with i.i.d contexts. The key to this result is characterizing the proportion of measurements DTS dedicates to each arm asymptotically. Because DTS adjusts how future measurements are collected as it learns about each arm, these limiting ratios depend on the true (and initially unknown) parameter vectors. The way DTS adapts its measurement effort is shown to maximize the asymptotic speed of learning: in a sense made formal later, the posterior probability assigned to the true best arm converges to one at an exponential rate and with the best possible exponent. DTS also minimizes the average sample size required to attain a vanishing simple regret. That result is a fully “frequentist” guarantee. The results in this section build on recent analyses of top-two sampling algorithms due to [1]}, [2]} and [3]} as well as lower bound techniques of [4]} and [5]}.
